I Need Step By Step Solution To Q. 4 And Q. 5.

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{We} \mathrm{have} \\ {\left(\mathrm{a}-\mathrm{b}\right)}^{\mathrm{n}}, \mathrm{n}\ge 5 \\ \mathrm{According} \mathrm{to} \mathrm{question}: \\ {\mathrm{T}}_5+{\mathrm{T}}_6=0 \\ {\Rightarrow }^{\mathrm{n}}{\mathrm{C}}_4 {\mathrm{a}}^{\mathrm{n}-4}.{\mathrm{b}}^4{-}^{\mathrm{n}}{\mathrm{C}}_5 {\mathrm{a}}^{\mathrm{n}-5}.{\mathrm{b}}^5=0 \\ {\Rightarrow }^{\mathrm{n}}{\mathrm{C}}_4 {\mathrm{a}}^{\mathrm{n}-4}.{\mathrm{b}}^4{=}^{\mathrm{n}}{\mathrm{C}}_5 {\mathrm{a}}^{\mathrm{n}-5}.{\mathrm{b}}^5 \\ \Rightarrow \frac{\mathrm{n}\left(\mathrm{n}-1\right)\left(\mathrm{n}-2\right)\left(\mathrm{n}-3\right)}{4\times 3\times 2\times 1}.\frac{{\mathrm{a}}^{\mathrm{n}}}{{\mathrm{a}}^4}.{\mathrm{b}}^4=\frac{\mathrm{n}\left(\mathrm{n}-1\right)\left(\mathrm{n}-2\right)\left(\mathrm{n}-3\right)\left(\mathrm{n}-4\right)}{5\times 4\times 3\times 2\times 1}.\frac{{\mathrm{a}}^{\mathrm{n}}}{{\mathrm{a}}^5}.{\mathrm{b}}^5 \\ \Rightarrow 1=\frac{\left(\mathrm{n}-4\right)}{5}.\frac{1}{\mathrm{a}}.\mathrm{b} \\ \frac{\mathrm{a}}{\mathrm{b}}=\frac{\mathrm{n}-4}{5} \end{gathered}$$

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